Had that conversation with another member over the weekend.
Spent 16 years working with ARRL Incoming QSL Bureau; so I have some idea about bureaus. Put in 8 to 16 hours a month just keeping up with the sorting and mailing. Incoming QSLs at Bureau have fallen off by as much as 50% or more in past 16 years ; undoubtedly due to LoTW, Eqsl, QRZ.com, HRD and other such services.
To put it plain and simple as I can, it's not a feasible idea because of the costs and time involved in the sorting and mailing of the cards. Someone would have to sacrifice many hours of their time to organize and keep it running. The cost of international postage would have to be charged to someone and I doubt the PODXS has sufficient funds to fund such an operation.
Think it would be best to use ARRL Outgoing Bureau or try to ship cards to various DX Bureaus. BTW, ARRL Outgoing/Incoming Bureaus only accept QSLs for USA stations if they're coming from DX stations outside U.S.; so if you send QSLs to other stations in US you will have to use snail mail.
Please note that there are many DX countries which do not have bureaus , but if they do they require that stations in that be members (like Germany , DARC Bureau, only members cab receive QSLs ... have had a number a returned QSLs recently from DARC). Add to this the fact that bureaus are notoriously slow and one can wait a year or more for their QSL to be answered. (My record is 38 years from a Russian !)
PODXS running its own bureau would be ill-advised and would certainly be a large money sucking hole. This is probably something has looked into at one time or another .
Hope I covered this subject. It's 4 am here and I'm probably not to coherent.
Jerry N9AVY #454
Have the higher ups ever considered starting a QSL Bureau for 070?